In an inkjet printer, letters and images are created by squirting drops of ink h

Question

In an inkjet printer, letters and images are created by squirting drops of ink horizontally at a sheet of paper from a rapidly moving nozzle. The pattern on the paper is controlled by an electrostatic valve that determines at each nozzle position whether ink is squirted onto the paper or not. The ink drops have a mass m = 1 .00x10'11 kg each and leave the nozzle and travel horizontally toward the paper at velocity v = 20.0 m/s . The drops pass through a charging unit that gives each drop a positive charge q by causing it to lose some electrons. The drops then pass between parallel deflecting plates of length Do = 1.75 cm , where there is a uniform vertical electric field with magnitude E = 7.70x104 N/C . If a drop is to be deflected a distance d = 0.320 mm by the time it reaches the end of the deflection plate, what magnitude of charge q must be given to the drop? Assume that the density of the ink drop is 1000 kg/m'J . and ignore the effects of gravity. Express your answer numerically in coulombs.

Explanation / Answer

As there will be force in the direction of electric field only, hence along the length of plate drop will move with constant velocity i.e. 20m/S hence time taken to cover 1.75 cm is t= 8.75×10^-4 sec.

In electric field direction, d is 0.320mm, initial velocity is zero, time taken is same, a = qE/m.

S = it+ 1/2at2. Hence d = 1/2qEt2/m.

Hence putting all values you will get q = 1.085×10^-15 C.

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